The inverse Laplace transform of the functionF ( s ) = (7s)/[( s − 1 ) ( s + 6 ) ]is a function of the form f ( t ) = A e^t + Be^(− 6 t) .a) Find the value of the coefficient Ab) Find the value of the coefficient B

Answers

Answer 1

To find the coefficients A and B in the inverse Laplace transform of F(s), we need to use partial fraction decomposition and the properties of Laplace transforms. Here's how we do it:

First, we factor the denominator of F(s) as (s-1)(s+6). Then we write F(s) as a sum of two fractions with unknown coefficients A and B:

[tex]F(s) = \frac{7s}{(s-1)(s+6)} = \frac{A}{s-1} +\frac{B}{s+6}[/tex]

To find A, we multiply both sides by (s-1) and then take the inverse Laplace transform:

[tex]L^{-1} [F(s)] = L^{-1}[\frac{A}{s-1} ] +L^{-1}[\frac{B}{s+6} ][/tex]
[tex]f(t) = A e^t + B e^{-6t}[/tex]

Since we know that the inverse Laplace transform of F(s) has the form of f(t) = A e^t + B e^(-6t), we can use this expression to solve for A and B. We just need to evaluate f(t) at two different values of t and then solve the resulting system of equations.

Let's start with t=0:

[tex]f(0) = A e^0 + B e^{0}  = A + B[/tex]

Now let's take the derivative of f(t) and evaluate it at t=0:

[tex]f'(t) = A e^{t} - 6B e^{-6t}[/tex]
f'(0) = A - 6B

We can now solve the system of equations:

A + B = f(0) = 0   (since F(s) is proper, i.e., has no DC component)
A - 6B = f'(0) = 7

Solving for A and B, we get:

A = 21/7 = 3
B = -21/7 = -3

Therefore, the coefficients in the inverse Laplace transform of F(s) are:

A = 3
B = -3

Learn more about Laplace here:

https://brainly.com/question/31481915

#SPJ11


Related Questions

what is the value of the expression -3y/x
when x = 12 and y=-8

Answers

Step-by-step explanation:

here is your answerr.

Was it helpful?

comment down

If there is any kind of suspicious mistake

then sorry

Whoever answers this question first gets brainly 2

Answers

Answer: H. 75
Explanation step by step:


Solve and graph the inequality.
7n - 1 > 76

Answers

Answer:

n>11

Step-by-step explanation:

I don't know how to graph this answer, sorry!

The solution of the inequality 7n - 1 > 76 gives n < 11 along with the graph.

Given Inequality:

7n - 1 > 76

To solve the inequality add 1 on both side of inequality as

7n - 1 + 1 > 76 + 1

7n > 77

Now, divide the inequality by 7 as

7n/ 7 > 77/ 7

n > 11.

Therefore, the solution is n > 11.

Learn more about Inequality here:

https://brainly.com/question/28823603

#SPJ6

Look at the photo below.

Answers

Answer:

complement, 70; supplement, 160*

Step-by-step explanation:

A yellow ball, a red ball, a white ball and a
black ball are placed in a barrel. Two balls
are drawn out of the barrel at random. What is the probability
that the yellow ball is drawn first?

Answers

Answer:

1/4 chance (this is equal to 25% as a percentage or 0.25 as a decimal)

Step-by-step explanation:

There are 4 balls and only one can be first. As there is only 1 yellow ball, there is 1/4 chance that the yellow ball is picked first.

Multiplying positive and negative fractions how do you do it ​

Answers

Answer:

I GOTCHU BAEE

Step-by-step explanation:

its just like regular negative numbers

but with fractions

see:

-7/12 x 1/2 = -7/24

negative negates the negative

negative negates the positive

positive keeps the positive positive

For a year, a chef from a restaurant collected data about the cost of strawberries and cherries in his local food market. this data is summarized in the table below. based on the data collected, select all of the statements that are correct.

Answers

Answer:

A Strawberries generally cost less.

D If the chef pays $6.00 for a pound of fruit, it is most likely cherries.

Step-by-step explanation:

A and D

15 points, 8-9 grade work

Polynomials

P(x) = 2x^4 + 3x^2 - 5x + 7

q(x) = -2x^2 + 4x - 3

calculation:

A. p(x) + q (x)

B. 2 • p (x)

C. p (x) - q (x)

D. 3 • p (x) + 4 • q (x)

E. p (x) • q (x)

F. (P (x) ) ^2

Answers

Answer:

A. p(x) + q (x) =2x^4 + 3x^2 - 5x + 7-2x^2 + 4x - 3 =2x+x²-x+4

B. 2 • p (x)=2(2x^4 + 3x^2 - 5x + 7)=4x+6x²-10x+14

C. p (x) - q (x) =2x^4 + 3x^2 - 5x + 7-(-2x^2 + 4x - 3 )=2x^4 + 3x^2 - 5x + 7+2x²-4x+3=2x+5x²-9x-2

D. 3 • p (x) + 4 • q (x) =3(2x^4 + 3x^2 - 5x +7)+4(-2x^2 + 4x - 3 )=6x⁴+9x²-15x+21-8x²+16x-12=6x⁴++x+9

E. p (x) • q (x)=sorry it is quite long.

F. (P (x) ) ^2this too.

heyy could you help me out with this question I have been stuck in this question??​

Answers

Answer:

true, false, true that is the answer I belive

Can 4(x+2)=10 equal 0

Answers

Answer:

x = 0.5

Step-by-step explanation:

The given expression is :

4(x+2) = 10

Using commutative property at LHS.

4x+8 = 10

Subtract 8 from both sides.

4x+8-8 = 10-8

4x = 2

x = (1/2) = 0.5

So, the value of x is equal to 0.5 instead of 0. Hence, the given expression cannot be equal to 0.

There were 24 people invited to a pizza party. One-fourth of the people wanted sausage and olives. Three-fourths
wanted plain cheese. How many plain pizzas should Sam order?


18,16,14?

Answers

Answer:

the  number of plain pizza does sam order is 18

Step-by-step explanation:

The computation of the number of plain pizza does sam order is shown below:

= Total people invited to a pizza party × plain cheese

= 24 × 3 ÷ 4

= 18

Hence, the  number of plain pizza does sam order is 18

-6=3x+3
Does anyone know this answer

Answers

Answer:

-1 :)

Step-by-step explanation:

Move all terms that don't contain x to the right side and solve.

x = −1

6.) Resuelve: 6(X + 8) - 30 + 7 = 49​

Answers

Answer:

x=4

Step-by-step explanation:

6(x+8)-30+7=49

6x+48-30+7=49

6x=49-48+30-7

6x=1+23

6x=24

x=[tex]\frac{24}{6}[/tex]

x=4

Step-by-step explanation:

Para resolver esto yo use una app llamada m a t h w a y

(sin los espacios) esta puede estar en varios idiomas, aunque esto se modifica segun el idioma en donde la uses.

6(x+8) -30+7 = 49                           1. Simplifica 6(x+8) -30+7

6x+25 = 49                                     2. Mueve todos los términos que no

                                                   contengan x al lado derecho de la ecuación

6x = 24                                           (25 pasa restando por lo cual sería, 49-25

                                                       que es igual a 24.)

                                                       3. Divide cada término por 6 y simplifica.

x = 4

Espero esto haya ayudado!

                                                     

tysm for whoever helps !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!11

Answers

Answer:

21

Step-by-step explanation:

When you simply the fractions down, you will get this

[tex]16 + 5 = 21[/tex]

Hope this Helped

How many fluid ounces are in 1 quart? With work!

Answers

Answer: 32 fluid ounce = 1 quart

Hey I'm sorry. I don't know if there are any work to show for this but I will try.

1 quart=2pints

2pints=4cups

4cups=32 fl oz

This is all the work I could show for this problem, you really should memorize this though 32 fl oz in a quart, it is very useful real life information :)

Use the distributive property to find the equivalent expression.
3(2 + x) =__+__x

Answers

Answer:

6+3x

Step-by-step explanation:

multiply each term in the parentheses by the outer term.

6 + 3x

3(2+x) is factored form
So you need to turn it back into standard form

HELP HELP HELP PLSSS

Answers

Answer:

option. c. 720°

.....................

Answer:

720degrees

Step-by-step explanation:

− 2/3m = −1/2 solve for m

Answers

Answer:

m=-18

Step-by-step explanation:

-12=2/3m

geometry: help needed, it’s urgent!
angle 1 measures 75 degrees, is this table right?

Answers

Answer:

angle 1 and 3 are alternate INTERIOR angles cos they are on the inside of the lines but you were close

If g(x) = 2x – 9, determine g(4) – g(1)

Answers

Step-by-step explanation:

g(x) = 2x - 9

g(4) = 2* 4 - 9

= 8 - 9

= - 1

g(1) = 2 * 1 - 9

= 2 - 9

= - 7

Now

g(4) - g(1)

= - 1 - ( -7)

= - 1 + 7

= 6

Hope it will help :)

If corresponding angles are on parallel lines, then their measure is the same _____.

always
never
sometimes

Answers

Step-by-step explanation:

always .

plz mark my answer as brainlist.hope this will be helpful to you

Answer: Always

Step-by-step-sumsum:

help me plz plz i need my grades up​

Answers

Answer:

Decimal: 2.1

Fraction: 21/10

Answer:
2.1
Explanation

Find The Area of the parallelogram...

Answers

Answer:

162 ft^2

Step-by-step explanation:

the formula for finding the area of a triangle is [tex]\frac{b*h}{2}[/tex]

the base is 27 and the height is 12

[tex]\frac{27*12}{2}=\frac{324}{2} = 162[/tex]

the area of a triangle is (base X height)/2

(27 X 12)/2 = 324/2 = 162ft^2

I need help I am really struggling with math

Answers

Answer:

Okay what is it i might be able to help

Step-by-step explanation:

-(7p+6)-2(-1-2p)
what is that simplified?

Answers

Answer:

-3p-40

Step-by-step explanation:

-(7p+6)-2(-1-2p)

-7p-42+2+4p

-3p-40

HELP ASAP HELPPP MARKING BRAINLIEST

Answers

The answer is 68 1/8

Answer:

answer is 68 1/8

Step-by-step explanation:

Rule: multiply by 2 Pattern: 3,6,12,24,48 Observation: Observation = something similar about the numbers

Answers

Step-by-step explanation:

This numerical sequence corresponds to a geometric progression, which occurs when there is a multiplication of the sequence numbers for a common reason whose result will always be the successor number of the numerical sequence.

Like for example:

3,6,12,24,48

The common reason for the geometric progression is the number 2, so the first term of the sequence multiplied by 2 will be equal to the second term of the sequence and so on:

3x2 = 6

6x2 = 12

12x2 = 24

24x2 = 48

It is necessary to emphasize that the ratio of a geometric progression will always be constant and will always be a number other than zero.

Kunal told Ana he was going to drop 10 dimes on the table. He said he would give her all the dimes where the "head" side was showing.How many dimes would Ana most likely get?

Answers

Answer:

10

Step-by-step explanation:

find the distance between j and k

Answers

Answer:

theres no picture...or points...

Step-by-step explanation:

randy needs to save 2550$ for a vacation. he has 6 months to save the money. how much money must he save each month?

Answers

Answer:

425

Step-by-step explanation:

2550/6=425

Answer:

425

Step-by-step explanation:

Other Questions
Michael must pay his way through college. He is a sophomore in high school and currently babysits regularly on the weekends. He works 15 hours and makes $8.00 an hour. He will be eligible to work at his uncle's restaurant in three months, and he can work twenty hours a week at $an hour. Use the PACED decision-process to decide what Michael's best choice is. Show each step. Which answer best describes how the cotton gin changed cotton farming?A. The cotton gin caused cotton prices to drop because it could be harvested so easily.B. The cotton gin added to the already high cost of producing cotton, and lowered demand.C. The cotton gin made it easier to remove seeds from cotton, but destroyed the rest of the plant.D. The cotton gin made growing cotton very profitable and increased the demand for slave labor. 15 POINTS!!answer the question in the picture Select the pair of terms that are NOT like terms. a) 3x2 , 3x3 b) -7xy, -9yx c) 8b, -0.5b d) -p2q2 , (pq)2 Find the missing angle.2080 Substitute a pronoun for the noun or noun phrase in italics.Mary, Bob, Sarah, and I are going shopping. At the end of When Birds Get Flu and Cows Go Mad!, author John DiConsiglio leaves what problem unresolved?whether the US should do more testing on cowswhether mad cow disease is likely to affect the readerwhether European countries should do more testing on cowswhether mad cow disease is likely to become a widespread problem Markus receives dollar bills from his grandfather for one week. On The first day he received a one dollar. On the second day he received two dollars on the third day he received four dollars and on the fourth day he received eight dollars if continues how much money will Markus have by the end of the week. Wright a 150-word paragraph in which you consider the effect of the black power movement on the nonviolent protest movement in the late 1960s el pez utiliza energa Please help I need it ASAP!! x 4y = 273x + y = -23 Answer the question provided in the picture below. This is middle school math btw, not college. 10 POINTS and WILL MARK AS A Brainlest PLEASE 12345678910= if i get the right answer i will give brainlistWhich point on the scatter plot is an outlier? Point A Point B Point C Point D According to the tow of conservation of matter, we know that the total number of atoms does not change in a chemical reaction and thus mas is conserved Thisis part of a chemical reaction hydrogen plus orygon yobis water Can you complete this moder? Reorganize the reactants in order to complete the productieof the reactionYour answer: Que son las caracteristicas literarias de una crnica? HURRYY PLEASE Which technology can observe electromagnetic radiation and avoid light pollution to allow for exploration beyond our solar system?A. space probeB. space stationC. space shuttleD. space observatory